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ROT_MAT and ORIGIN CHANGE - Rotation Angle
The rotation angle in 4-axis machines is calculated as follows:
Rotation angle = ATAN (*_ORIGIN / Z_ORIGIN)
where * is I or J.
To obtain the appropriate result, it is recommended to:
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use FORTRAN ATAN2 function (in external process) and not the ATAN function in the EXF file.
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define I,J,K_ORIGIN with a precision of 7 decimal places.
The external program may be written as follows:
SUBROUTINE UGPSUB (NAME, L)
CHARACTER*6 NAME
INTEGER L
IF (NAME(1:L) .EQ. 'ATANG2') THEN
CALL ATANG2
ELSEIF . . . .
.
.
.
ENDIF
RETURN
END
C------------------------------------------------
SUBROUTINE ATANG2
C
C H-horizontal value
C V-vertical value
C A-angle result
REAL H,V,A
C
CALL GTEPGP ('H',H)
CALL GTEPGP ('V',V)
C
A = ATAN2 (V,H)
C
C Convert the angle from radians to degrees
C
A = A*180.0/3.1415926
C
C The conversion may vary between machines, according to the machine type.
C (Some machines may use angles 0-360 or +/-180 . . .)
C
CALL STEPGP('A',A)
RETURN
END
C------------------------------------------------
External programs like the one displayed above may be called from the EXF file by using the CALL command:
V = I_ORIGIN; H = K_ORIGIN;
CALL "ATANG2" INPAR H V ; OUTPAR A;
YROTATION = A;
Rotation angles in 5-axis machines (rotated table) may be calculated as follows:
1st rotation angle = ATAN ( *_ORIGIN / *_ORIGIN )
2nd rotation angle = ATAN ( *_ORIGIN / (*_ORIGIN * COS [1st rotation angle]))
where * is I, J, or K according to the machine geometry, and ATAN is used as described for 4-axis machines.
The rotation of the first axis affects the *_ORIGIN of the two other axes. This rotation and the first axis to be rotated vary between the machine types.
ROT_MAT1 . . . ROT_MAT9
As explained in this manual, ROT_MAT1. . .ROT_MAT9 are values of MATRIX (3,3). All coordinates are multiplied by that matrix before "sending" to the post.
The UNIT matrix may be initialized at BEGINNING OF TAPE:
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ROT_MAT1=1; |
ROT_MAT2=0; |
ROT_MAT3=0; |
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ROT_MAT4=0; |
ROT_MAT5=1; |
ROT_MAT6=0; |
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ROT_MAT7=0; |
ROT_MAT8=0; |
ROT_MAT9=1; |
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TRANS_MATX=0; |
TRANS_MATY=0; |
TRANS_MATZ=0; |
After finding the rotation angle (A), ROT_MAT* values should be updated as follows:
Rotation around X axis:
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ROT_MAT1=1; |
ROT_MAT2=0; |
ROT_MAT3=0; |
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ROT_MAT4=0; |
ROT_MAT5=COS(A); |
ROT_MAT6=-SIN(A); |
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ROT_MAT7=0; |
ROT_MAT8=SIN(A); |
ROT_MAT9=COS(A); |
Rotation around Y axis:
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ROT_MAT1=COS(A); |
ROT_MAT2=0; |
ROT_MAT3=-SIN(A); |
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ROT_MAT4=0; |
ROT_MAT5=1; |
ROT_MAT6=0; |
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ROT_MAT7=SIN(A); |
ROT_MAT8=0; |
ROT_MAT9=COS(A); |
Rotation around Z axis:
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ROT_MAT1=COS(A); |
ROT_MAT2=SIN(A); |
ROT_MAT3=0; |
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ROT_MAT4=-SIN(A); |
ROT_MAT5=COS(A); |
ROT_MAT6=0; |
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ROT_MAT7=0; |
ROT_MAT8=0; |
ROT_MAT9=1; |
Translation Values - TRANS_MAT
The rotation causes the tool end point to move from its original location. Therefore, a translation must be performed to cancel this error.
The translation values are calculated as follows:
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Find the physical distance (X, Y and Z) between the origin and the rotation axis, as it will be on the machine.
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Rotate those values using the rotation matrix (ROT_MAT1 . . ROT_MAT9).
If the part rotates (rotating table), the physical distance between the origin and rotation axis may be calculated using the following parameters:
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distance between a fixed point on the machine table and the rotation axis (a fixed value depending on the machine geometry)
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distance between the MACSYS (MODEL) and the fixed point. Use the POST interaction ENTER MACH.ZERO, and the GPP parameters X_MACH, Y_MACH and Z_MACH.
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distance between the MACSYS (MODEL) and the origin, GPP parameters X_ORIGIN, Y_ORIGIN and Z_ORIGIN.
If the tool rotates (rotating head), the physical distance between the origin and the rotation axis may be calculated using the following parameters:
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distance between the face of the spindle and the rotation axis (a fixed value depending on the machine geometry).
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distance between the tool end point and the face of the spindle.
Use the parameter GAUGE LENGTH in the tool definition and the GPP parameter GAUGE_LEN. As the GAUGE_LEN parameter changes with the tool change, the translation parameters TRANS_MATX . . . TRANS_MATZ must be updated every tool change.
Translation Values - ORIGIN CHANGE (Translation Only)
When TRANS_MAT values are 0, the coordinates are expressed in the current origin coordinate system. To express the coordinates in another origin coordinate system (i.e., the first one), update TRANS_MAT values as follows:
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Save the X,Y,Z_ORIGIN of the first origin (i.e., first X,Y,Z).
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Calculate the TRANS_MAT values:
TRANS_MATX = X_ORIGIN - FIRSTX
TRANS_MATY = Y_ORIGIN - FIRSTY
TRANS_MATZ = Z_ORIGIN - FIRSTZ
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